Transcending the Rayleigh Hypothesis with multipolar sources distributed across the topological skeleton of a scatterer

There is an ever-growing need to study the optical response of complex photonic systems involving multi-scattering phenomena with strong near-field interactions. Since fully numerical methods often imply high computational costs, semi-analytical methods are preferred. However, most semi-analytical methods are commonly plagued by what is known as the problem of the Rayleigh Hypothesis: they typically use analytical representations of the scattered fields that are invalid in the near-field region of the scatterer. In this work, we present an alternative representation scheme for the scattered fields based on a distribution of multipolar sources across the topological skeleton of the scatterer. We demonstrate how such a representation overcomes the problem of the Rayleigh Hypothesis for scatterers of arbitrary geometry. In that regard, our work enriches the available toolkit of semi-analytical methods in light-scattering by pushing decisively against one of the fundamental limitations of the existing methods.